(n-2)(n+6)+15=0

Solution for (n-2)(n+6)+15=0 equation:

Simplifying
(n + -2)(n + 6) + 15 = 0

Reorder the terms:
(-2 + n)(n + 6) + 15 = 0

Reorder the terms:
(-2 + n)(6 + n) + 15 = 0

Multiply (-2 + n) * (6 + n)
(-2(6 + n) + n(6 + n)) + 15 = 0
((6 * -2 + n * -2) + n(6 + n)) + 15 = 0
((-12 + -2n) + n(6 + n)) + 15 = 0
(-12 + -2n + (6 * n + n * n)) + 15 = 0
(-12 + -2n + (6n + n2)) + 15 = 0

Combine like terms: -2n + 6n = 4n
(-12 + 4n + n2) + 15 = 0

Reorder the terms:
-12 + 15 + 4n + n2 = 0

Combine like terms: -12 + 15 = 3
3 + 4n + n2 = 0

Solving
3 + 4n + n2 = 0

Solving for variable 'n'.

Factor a trinomial.
(3 + n)(1 + n) = 0

Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 0

Move all terms containing n to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + n = 0 + -1
n = 0 + -1

Combine like terms: 0 + -1 = -1
n = -1

Simplifying
n = -1
Solution
n = {-3, -1}